Difference between revisions of "HEDP notes"

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[https://wiki.iac.isu.edu/index.php/RS#Pulsed-power_applications_.282-LTD-driver_and_more.29 go back]
 
[https://wiki.iac.isu.edu/index.php/RS#Pulsed-power_applications_.282-LTD-driver_and_more.29 go back]
  
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=high energy density plasma defined as a plasma with pressure above 1 MBar=
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=high energy density plasma is a plasma with pressure above 1 MBar=
 
<math>1 MBar = 1 \times 10^6 \times 10^5 Pa = 10^{11} Pa = 10^{11} (N m)/(m^2) = 10^{11} J/m = 10^{11} (10^7 erg)/(10^6 cm^3) = 10^{12} erg/cm^3</math>
 
<math>1 MBar = 1 \times 10^6 \times 10^5 Pa = 10^{11} Pa = 10^{11} (N m)/(m^2) = 10^{11} J/m = 10^{11} (10^7 erg)/(10^6 cm^3) = 10^{12} erg/cm^3</math>
  
  
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=magnetic field produced by single wire (Ampere law / Biot-Savart Law)=
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=magnetic field produced by single wire (Biot-Savart Law)=
  
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  <math>B[G] = 0.2 \times I(A) / r(cm) </math>
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  <math>B[T] = \mu I / ( 2\pi r ) </math>
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<math>B[T] = 0.2 \times I(kA) / r(mm) </math>
 
  
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*100 kA at 1 mm radius is 20 T
 
 
*10 MA at 4 mm radius is 500 T
 
*10 MA at 4 mm radius is 500 T
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*100 kA at 1 um radius is 20 kT
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*100 kA at 40 um radius is 500 T
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*160 kA at 5 um radius is 6,400 T
  
 +
=magnetic pressure=
  
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=magnetic pressure=
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<math> P_m(bar) = 4 \times B(T)^2 </math>
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<math> P_m(bar) = 0.16 \times I(kA)^2 \times R(mm)^{-2} </math>
  
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<math> P_m(bar) = (2 \times B[T])^2 = I^2 \times R^{-2} </math>
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*10 MA at 4 mm radius is 1 MBar
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<math> P_m(bar) = 0.16 \times I^2 \times R^{-2} </math>
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*100 kA at 40 um radius is 1 MBar
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*160 kA at 5 um radius is 164 MBar
  
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<math> 5 \times 10^6 G \Rightarrow 1 MBar </math>
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=Bennett condition=
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*magnetic pressure = plasmakinetic pressure
  
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<math> 200 \times 10^6 G \Rightarrow 1,600 MBar </math>
 
  
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*14 MBar at 140 kA at 15-um radius (shot 634 with 2x30-um W wires)
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*25 MBar at 150 kA at 12-um radius (shot 657 with 2x30-um Mo wires)
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*100 MBar at 154 kA at 6-um radius (shot 657 with 2x30-um Mo wires)
  
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=Bennett condition=
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=Links=
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* magnetic pressure = plasmakinetic pressure
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*[http://www.nap.edu/read/10544/chapter/1 Frontiers in High Energy Density Physics THE X-GAMES OF CONTEMPORARY SCIENCE]
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* so our plasma pressure (at 100 kA at 1 um radius) is about 1,600 MBar (wau!! really??!!)
 

Latest revision as of 18:13, 31 May 2017

go back

high energy density plasma is a plasma with pressure above 1 MBar

[math]1 MBar = 1 \times 10^6 \times 10^5 Pa = 10^{11} Pa = 10^{11} (N m)/(m^2) = 10^{11} J/m = 10^{11} (10^7 erg)/(10^6 cm^3) = 10^{12} erg/cm^3[/math]


magnetic field produced by single wire (Biot-Savart Law)

[math]B[T] = \mu I / ( 2\pi r ) [/math]
  • 10 MA at 4 mm radius is 500 T
  • 100 kA at 40 um radius is 500 T
  • 160 kA at 5 um radius is 6,400 T

magnetic pressure

[math] P_m(bar) = 4 \times B(T)^2 [/math]
[math] P_m(bar) = 0.16 \times I(kA)^2 \times R(mm)^{-2} [/math]
  • 10 MA at 4 mm radius is 1 MBar
  • 100 kA at 40 um radius is 1 MBar
  • 160 kA at 5 um radius is 164 MBar

Bennett condition

  • magnetic pressure = plasmakinetic pressure


  • 14 MBar at 140 kA at 15-um radius (shot 634 with 2x30-um W wires)
  • 25 MBar at 150 kA at 12-um radius (shot 657 with 2x30-um Mo wires)
  • 100 MBar at 154 kA at 6-um radius (shot 657 with 2x30-um Mo wires)

Links

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